Okay, the problem with percentages is, that you can't just "split them in half". Percentages are relative to something. In this case, the 20% discount is relative to the pricetag, while the 20% profit is relative to the $80 Harry buys toolkits for.
So, he wants to make 20% profit.
This means he wants to receive 0.20*80+80=$96
This does not yet include the discount.
Then he wants to price it as such, that once the discount is calculated, what is left over is $96.
This means $96 is equal to 80% (100%-20%)
Therefore you need to solve 0.80*x=$96, and x is the price that goes on the price tag.
Does this make it clear?